## Intermediate Algebra (12th Edition)

$\sqrt{11}$
$\bf{\text{Solution Outline:}}$ To rationalize the given radical expression, $\dfrac{11}{\sqrt{11}} ,$ multiply both the numerator and the denominator by an expression that will make the denominator a perfect power of the index. $\bf{\text{Solution Details:}}$ Multiplying both the numerator and the denominator by an expression that will make the denominator a perfect power of the index results to \begin{array}{l}\require{cancel} \dfrac{11}{\sqrt{11}}\cdot\dfrac{\sqrt{11}}{\sqrt{11}} \\\\= \dfrac{11\sqrt{11}}{\sqrt{11}(\sqrt{11})} .\end{array} Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{11\sqrt{11}}{\sqrt{11(11)}} \\\\= \dfrac{11\sqrt{11}}{\sqrt{11^2}} \\\\= \dfrac{11\sqrt{11}}{11} \\\\= \dfrac{\cancel{11}\sqrt{11}}{\cancel{11}} \\\\= \sqrt{11} .\end{array}